Van Bommel was appointed only weeks after Belgium’s quarter-final exit at the World Cup effectively cost Rudi Garcia his job with the French-born coach and the Belgian federation agreeing not to renew his deal.
Van Bommel was quickly appointed to replace him and Courtois said the former Dutch international would enjoy the respect of his new charges.
"It wasn't really a surprise because his name had been circulating for quite a while," Courtois told reporters at a sponsorship event.
"I think he proved at Antwerp that he's a top coach. A lot of the players speak very positively about him, so I'm looking forward to getting to know him.
"The most important thing is that Van Bommel himself played at the highest level and knows what it's like to play matches like these.
"That top-level experience is definitely a positive and it naturally earns a lot of respect from the players," he said.
Whether the 34-year-old Courtois himself will actually play under Van Bommel remains uncertain.
After the World Cup, the Real Madrid goalkeeper said that he would like to continue with Belgium but only if he was allowed to skip the upcoming Nations League campaign.
"After the World Cup, I definitely still want to continue, but it will depend on the conversation I have with him," Courtois said.
"I'd like to have some rest during the Nations League and we'll have to try to reach an agreement on that.
"After that, I'll decide whether I want to continue or not."
Courtois also reflected on Belgium's World Cup exit, which came after he was injured in the last-eight tie against Spain in Los Angeles on July 10 and his replacement Senne Lammens made an error to gift eventual champions Spain a 2-1 win.
Courtois later said he believed he could have continued and made the point again at the weekend.
"I just felt that I couldn't take goal kicks anymore.
"A defender could have taken them instead. During open play, I could still have made sideways passes.
"But the coach said: 'We agreed that only players who are 100% fit will play.' Fine, no problem."
Courtois said there was never any disagreement with Garcia, who was heavily criticised for many of his choices during the World Cup.
"Of course, I was disappointed because it was against Spain and we were in a good rhythm. But the team is more important than I am.
"The decision was made and there was never any bad blood. I never wanted to speak badly about him (Garcia)," he added.
FIFA World Cup 2026
The 2026 World Cup took place from June 11th to July 19th in the United States, Canada and Mexico. The tournament featured 48 national teams and was won by Spain, who beat Argentina in the final.
Full schedule and results | Group standings and bracket | Past winners of the tournament | Our team of the tournament | About the 2030 World Cup